To keep your white dog's coat around his eyes looking healthy and bright, you can do the following:

Trim the hair regularly: Regularly trimming the hair around the eyes will help prevent hair from getting into your dog's eyes and causing discomfort or irritation. It will also help keep the hair from getting too long and covering his eyes.

Clean regularly: Dirt and debris can accumulate around the eyes, so it's important to clean this area regularly with a mild cleanser designed for dogs to prevent stains and discoloration. You can find coat care products around the eyes here https://www.superiorcare.pet/collections/clear-eyes-solution

Use sunscreen: Exposure to the sun can cause discoloration and damage to the coat around your dog's eyes. Consider using a sunscreen specially formulated for dogs to protect this sensitive area.

Visit the vet: If you notice any changes in the coat around your dog's eyes, such as excessive redness, swelling or discharge, you should consult your vet to rule out any underlying health problems.